docs: update description

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stdlib-js · aayush0325 · Jun 26, 2025 · Jun 26, 2025 · Jun 26, 2025 · Jun 27, 2025
commit 47b35fd32df36c086cfa43d43146c0021e4e0f42
diff --git a/lib/node_modules/@stdlib/lapack/base/dlanv2/docs/types/index.d.ts b/lib/node_modules/@stdlib/lapack/base/dlanv2/docs/types/index.d.ts
@@ -48,10 +48,15 @@ interface Routine {
 	* ```tex
 	* \begin{bmatrix}
 	* \text{AA} & \text{BB} \\
-	* 0 & \text{DD}
+	* \text{CC} & \text{DD}
 	* \end{bmatrix}
 	* ```
 	*
+	* where either:
+	*
+	* -   `CC` = 0, `AA` and `DD` are the real eigenvalues of the matrix.
+	* -   `AA` = `DD` and `BB * CC` < 0, `AA + sqrt( BB * CC )` and `AA - sqrt( BB * CC )` are the complex conjugate eigenvalues.
+	*
 	* @param A - array containing the element A(1,1)
 	* @param B - array containing the element A(1,2)
 	* @param C - array containing the element A(2,1)
@@ -117,10 +122,15 @@ interface Routine {
 	* ```tex
 	* \begin{bmatrix}
 	* \text{AA} & \text{BB} \\
-	* 0 & \text{DD}
+	* \text{CC} & \text{DD}
 	* \end{bmatrix}
 	* ```
 	*
+	* where either:
+	*
+	* -   `CC` = 0, `AA` and `DD` are the real eigenvalues of the matrix.
+	* -   `AA` = `DD` and `BB * CC` < 0, `AA + sqrt( BB * CC )` and `AA - sqrt( BB * CC )` are the complex conjugate eigenvalues.
+	*
 	* @param A - array containing the element A(1,1)
 	* @param offsetA - index in `A` of the element A(1,1)
 	* @param B - array containing the element A(1,2)
@@ -197,10 +207,15 @@ interface Routine {
 * ```tex
 * \begin{bmatrix}
 * \text{AA} & \text{BB} \\
-* 0 & \text{DD}
+* \text{CC} & \text{DD}
 * \end{bmatrix}
 * ```
 *
+* where either:
+*
+* -   `CC` = 0, `AA` and `DD` are the real eigenvalues of the matrix.
+* -   `AA` = `DD` and `BB * CC` < 0, `AA + sqrt( BB * CC )` and `AA - sqrt( BB * CC )` are the complex conjugate eigenvalues.
+*
 * @param A - array containing the element A(1,1)
 * @param B - array containing the element A(1,2)
 * @param C - array containing the element A(2,1)

diff --git a/lib/node_modules/@stdlib/lapack/base/dlanv2/lib/base.js b/lib/node_modules/@stdlib/lapack/base/dlanv2/lib/base.js
@@ -71,10 +71,15 @@ var multpl = 4.0;
 * ```tex
 * \begin{bmatrix}
 * \text{AA} & \text{BB} \\
-* 0 & \text{DD}
+* \text{CC} & \text{DD}
 * \end{bmatrix}
 * ```
 *
+* where either:
+*
+* -   `CC` = 0, `AA` and `DD` are the real eigenvalues of the matrix.
+* -   `AA` = `DD` and `BB * CC` < 0, `AA + sqrt( BB * CC )` and `AA - sqrt( BB * CC )` are the complex conjugate eigenvalues.
+*
 * @private
 * @param {Float64Array} A - array containing the element A(1,1)
 * @param {NonNegativeInteger} offsetA - index in `A` of the element A(1,1)

diff --git a/lib/node_modules/@stdlib/lapack/base/dlanv2/lib/dlanv2.js b/lib/node_modules/@stdlib/lapack/base/dlanv2/lib/dlanv2.js
@@ -51,10 +51,15 @@ var base = require( './base.js' );
 * ```tex
 * \begin{bmatrix}
 * \text{AA} & \text{BB} \\
-* 0 & \text{DD}
+* \text{CC} & \text{DD}
 * \end{bmatrix}
 * ```
 *
+* where either:
+*
+* -   `CC` = 0, `AA` and `DD` are the real eigenvalues of the matrix.
+* -   `AA` = `DD` and `BB * CC` < 0, `AA + sqrt( BB * CC )` and `AA - sqrt( BB * CC )` are the complex conjugate eigenvalues.
+*
 * @param {Float64Array} A - array containing the element A(1,1)
 * @param {Float64Array} B - array containing the element A(1,2)
 * @param {Float64Array} C - array containing the element A(2,1)

diff --git a/lib/node_modules/@stdlib/lapack/base/dlanv2/lib/index.js b/lib/node_modules/@stdlib/lapack/base/dlanv2/lib/index.js
@@ -21,6 +21,38 @@
 /**
 * LAPACK routine to compute the Schur factorization of a real 2-by-2 nonsymmetric matrix `A` in standard form.
 *
+* Given a real 2×2 matrix:
+*
+* ```tex
+* \begin{bmatrix}
+* A & B \\
+* C & D
+* \end{bmatrix}
+* ```
+*
+* this routine computes an orthogonal matrix:
+*
+* ```tex
+* \begin{bmatrix}
+* \text{CS} & \text{SN} \\
+* -\text{SN} & \text{CS}
+* \end{bmatrix}
+* ```
+*
+* such that the matrix is reduced to Schur (quasi-triangular) form:
+*
+* ```tex
+* \begin{bmatrix}
+* \text{AA} & \text{BB} \\
+* \text{CC} & \text{DD}
+* \end{bmatrix}
+* ```
+*
+* where either:
+*
+* -   `CC` = 0, `AA` and `DD` are the real eigenvalues of the matrix.
+* -   `AA` = `DD` and `BB * CC` < 0, `AA + sqrt( BB * CC )` and `AA - sqrt( BB * CC )` are the complex conjugate eigenvalues.
+*
 * @module @stdlib/lapack/base/dlanv2
 *
 * @example

diff --git a/lib/node_modules/@stdlib/lapack/base/dlanv2/lib/ndarray.js b/lib/node_modules/@stdlib/lapack/base/dlanv2/lib/ndarray.js
@@ -51,10 +51,15 @@ var base = require( './base.js' );
 * ```tex
 * \begin{bmatrix}
 * \text{AA} & \text{BB} \\
-* 0 & \text{DD}
+* \text{CC} & \text{DD}
 * \end{bmatrix}
 * ```
 *
+* where either:
+*
+* -   `CC` = 0, `AA` and `DD` are the real eigenvalues of the matrix.
+* -   `AA` = `DD` and `BB * CC` < 0, `AA + sqrt( BB * CC )` and `AA - sqrt( BB * CC )` are the complex conjugate eigenvalues.
+*
 * @param {Float64Array} A - array containing the element A(1,1)
 * @param {NonNegativeInteger} offsetA - index in `A` of the element A(1,1)
 * @param {Float64Array} B - array containing the element A(1,2)